The focus of this thesis is the computational modelling of transition metal bimetallic (nanoalloy) clusters. More specifically, the study of Pd-Pt, Ag-Pt, Au-Au and Pd-Au as a few tens of atoms in the gas phase. The author used a combination of global optimization techniques - coupled with a Gupta-type empirical many-body potential - and Density Functional Theory (DFT) calculations to study the structures, bonding and chemical ordering, as well as investigate the chemisorptions of hydrogen and carbon monoxide on bimetallic clusters. This research is highly relevant to experimental catalytic studies and has resulted in more than seven publications in international journals.